Best answer: Yes. Switch Lite can run any Switch game which offers handheld mode, and Minecraft is one such game.
- Switch Lite is here: Nintendo Switch Lite ($200 at Amazon)
- Build your world: Minecraft for Switch ($29 at Amazon)
Switch, Switch Lite, and their games
Nintendo has stated that both the Switch and the Switch Lite will use the same physical game cartridges. As long as a game is playable in handheld mode, it will be compatible with the new handheld console. If you already have Minecraft on your Switch, you will be able to use it on your new Switch Lite as well.
Nintendo has no intention to make exclusive games for either the Switch or Switch Lite. This becomes apparent when you realize you can transfer not just your physical copies but also digital as well. According to the support page, "software purchased for download can be played on either console as long as the console is linked to the same Nintendo account."
What does this mean? Yes, you can play Minecraft on your Switch Lite, and your Switch, and you can seamlessly swap between the two if you'd like! For more detailed information about transferring saved game data Nintendo has a helpful support page on the matter.
Minecraft for Switch & Switch Lite
The port from PC to Switch went well with few changes. One of the most significant changes is the limitation of your world size. Moving from the PC and the larger consoles, they had to reduce the maximum world size to Medium. In terms of Minecraft, the medium is still quite large, but it is something to keep in mind. The draw distance was shortened just a bit for handheld as well. Neither of which has been an issue for me, especially considering the game runs at a clean 60 fps even in handheld.
So, if you want to play Minecraft on the Switch Lite, grab that handheld and build your heart out.
It's here!

Nintendo Switch Lite
Smaller, less expensive, just as much fun
Nintendo Switch Lite works solely in handheld mode, but it uses the same cartridges as the standard Nintendo Switch. Any of your games that offer handheld mode will be compatible, and it can link with Nintendo Switch to play local co-op games.
Build your world

Minecraft
Just watch out for creepers
Minecraft is an open-world voxel game you can play solo or with friends online. While the game is mostly a sandbox builder, regular maintenance is done, and updates are added to flesh out the world with new items and animals.
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